A book decomposition of a manifold is a way of decomposing it as a union of codimension-1 submanifolds (the pages) that are glued along a codimension-2 submanifold (the binding). For example, each fibered knot gives a book decomposition of the 3-sphere. More generally, every odd dimensional manifold has a book decomposition by work of Alexander, Lawson, and Quinn. In this talk I’ll explain why even-dimensional hyperbolic manifolds do not have book decompositions. The main tool is Morse complexity, a norm on singular homology introduced by Gromov for which we give some new computations. This is joint work with Fedya Manin and Shmuel Weinberger.

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Last modified: Wed Oct 22 17:34:30 EDT 2025